We analyze the detection and interpretation of high fringe-density interferograms with CCD cameras. The high spatial frequencies beyond the Nyquist frequency of the CCD elements are shown in the recorded interferogram as fringes of lesser density and reduced contrast. This is due to the large sampling interval and intensity averaging over the pixel. We develop an analytic expression for the detected modulation intensity. It is seen to contain the phase information in its partial derivatives. We perform a simulation with a set of phase-shifted interferograms detected with finite pixel size to recover the detected modulation intensity. The phase is compared with the analytic expression resulting in the maximum error of less than 0.02 percent demonstrating the feasibility of the proposed model.